A Neat Trick

Here's a tough problem: Suppose you are the publisher of a paper and you want to get an estimate of the quality. In particular, you want to estimate how many unfound grammar and spelling errors remain in a paper after it has passed through your editing staff. How, you might ask, could we possibly know how many errors haven't been found if we never find them? That sounds so obviously impossible that it's stupid to ask! Right?

Wrong!

Here is one method. You take the paper before the editor sees it and purposely insert some errors, say 20 for simplicity's sake. Now give it to your editing staff. After working on it suppose that they find 50 errors, and that 18 of them were errors purposely inserted. Now you know that the editors found 90% of your inserted errors and you have a basis for knowing that they find about 90% of all errors. Therefore, since they found 32 real errors you can reasonably believe that there are still 3 or 4 real errors remaining (32 / 9 * 10 = 35.55 ...).

I think that's a neat trick to accomplish what is obviously impossible to know.